Universal Local Operator Quenches and Entanglement Entropy

TL;DR

This paper introduces a new class of local quenches described by mixed states, analyzing entanglement entropy evolution in holographic and Dirac fermion CFTs, revealing both known and novel behaviors.

Contribution

It presents a universal parameterization of local quenches by mixed states and compares entanglement entropy dynamics in holographic and Dirac fermion CFTs, uncovering new phenomena.

Findings

Holographic CFT results match pure state quenches

Dirac fermion CFT exhibits new entanglement behaviors

Derived an upper bound for pure state quenches in Dirac fermion CFT

Abstract

We present a new class of local quenches described by mixed states, parameterized universally by two parameters. We compute the evolutions of entanglement entropy for both a holographic and Dirac fermion CFT in two dimensions. This turns out to be equivalent to calculations of two point functions on a torus. We find that in holographic CFTs, the results coincide with the known results of pure state local operator quenches. On the other hand, we obtain new behaviors in the Dirac fermion CFT, which are missing in the pure state counterpart. By combining our results with the inequalities known for von-Neumann entropy, we obtain an upper bound of the pure state local operator quenches in the Dirac fermion CFT. We also explore predictions about the behaviors of entanglement entropy for more general mixed states.